Browsing Mathematics by Title
-
Simić, Slavko (Belgrade , 1997)[more][less]
-
Lukić, Mirko (Belgrade)[more][less]
-
Kulenović, Mustafa (Sarajevo)[more][less]
-
Popstanojević, Zoran (Belgrade , 1963)[more][less]
URI: http://hdl.handle.net/123456789/224 Files in this item: 1
phdZoranPopstojanovic.pdf ( 1.549Mb ) -
Muzika Dizdarević, Manuela (Beograd , 2017)[more][less]
Abstract: Subject of this doctoral thesis is the application of algebraic techniques on one of the central topics of combinatorics and discrete geometry - polyomino tiling. Polyomino tilings are interesting not only to mathematicians, but also to physicists and biologists, and they can also be applied in computer science. In this thesis we put some emphasis on possibility to solve special class of tiling problems, that are invariant under the action of nite group, by using theory of Gr obner basis for polynomial rings with integer coe cients. Method used here is re ecting deep connection between algebra, geometry and combinatorics. Original scienti c contribution of this doctoral thesis is, at the rst place, in developing a techniques which enable us to consider not only ordinary Z?tiling problems in a lattice but the problems of tilings which are invariant under some subgroups of the symmetry group of the given lattice. Besides, it provides additional generalizations, originally provided by famous mathematicians J. Conway and J. Lagarias, about tiling of the triangular region in hexagonal lattice. Here is a summary of the content of the theses. In the rst chapter we give an exposition of the Gr obner basis theory. Especially, we emphasize Gr obner basis for polynomial rings with integer coe cients. This is because, in this thesis, we use algorithms for determining Gr obner basis for polynomials with integer coe cients. Second chapter provides basic facts about regular lattices in the plane. Also, this chapter provides some fundamental terms of polyomino tiling in the square and hexagonal lattice. Third chapter of this thesis is about studying Ztilings in the square lattice, which are invariant under the subgroup G of the group of all isometric transformations of the lattice which is generated by the central symmetry. One of the steps to resolve this problem was to determine a ring of invariants PG and its generators and relations among them. We use Gr obner basis theory to achieve this. Forth chapter covers the analysis of Ztilings in the hexagonal lattice which are symmetric with respect to the rotation of the plane for the angle of 120 . Main result of the fourth chapter is the theorem which gives conditions for symmetric tiling of the triangular region in plane TN, where N is the number of hexagons on each side of triangle. This theorem is one of the possible generalizations of the well known result, provided by Conway and Langarias. Fifth chapter provides another generalization of Conway and Lagarias result, but this time it is about determining conditions of tiling of triangular region TN in the hexagonal lattice not only with tribones, but with nbones. nbone is basic shape of of n connected cells in the hexagonal lattice, where n is arbitrary integer. URI: http://hdl.handle.net/123456789/4503 Files in this item: 1
muzikadizarevic.manuela.pdf ( 33.23Mb ) -
Lazarević, Ilija (Belgrade)[more][less]
-
Lazović, Bojana (Beograd , 2018)[more][less]
URI: http://hdl.handle.net/123456789/4748 Files in this item: 1
B_Lazovic_Doktorska_disertacija.pdf ( 2.269Mb ) -
Jandrlić, Davorka (Beograd , 2016)[more][less]
Abstract: Application of association rule and support vector machine technique for T cell epitope prediction Abstract: Data mining is an interdisciplinary sub eld of computer science, including various scienti c disciplines such as: database systems, statistics, machine learning, arti cial intelligence and the others. The main task of data mining is automatic and semi-automatic analysis of large quantities of data to extract previously unknown, nontrivial and interesting patterns. Rapid development in the elds of immunology, genomics, proteomics, molecular biology and other related areas has caused a large increase in biological data. Drawing conclusions from these data requires sophisticated computational analyses. Without automatic methods to extract data it is almost impossible to investigate and analyze this data. Currently, one of the most active problems in immunoinformatics is T cell epitope identi cation. Identi cation of T - cell epitopes, especially dominant T - cell epitopes widely represented in population, is of the immense relevance in vaccine development and detecting immunological patterns characteristic for autoimmune diseases. Epitope-based vaccines are of great importance in combating infectious and chronic diseases and various types of cancer. Experimental methods for identi cation of T - cell epitopes are expensive, time consuming, and are not applicable for large scale research (especially not for the choice of the optimal group of epitopes for vaccine development which will cover the whole population or personalized vaccines). Computational and mathematical models for T - cell epitope prediction, based on MHC-peptide binding, are crucial to enable the systematic investigation and identi cation of T - cell epitopes on a large dataset and to complement expensive and time consuming experimentation [16]. T - cells (T - lymphocytes) recognize protein antigen(s) only when degradated to peptide fragments and complexed with Major Histocompatibility Complex (MHC) molecules on the surface of antigen-presenting cells [1]. The binding of these peptides (potential epitopes) to MHC molecules and presentation to T - cells is a crucial (and the most selective) step in both cellular and humoral adoptive immunity. Currently exist numerous of methodologies that provide identi cation of these epitopes. In this PhD thesis, discussed methods are exclusively based on peptide sequence binding to MHC molecules. It describes existing methodologies for T - cell epitope prediction, the shortcomings of existing methods and some of the available databases of experimentally determined linear T - cell epitopes. The new models for T - cell epitope prediction using data mining techniques are developed and extensive analyses concerning to whether disorder and hydropathy prediction methods could help understanding epitope processing and presentation is done. Accurate computational prediction of T cell epitope, which is the aim of this thesis, can greatly expedite epitope screening by reducing costs and experimental e ort. These theses deals with predictive data mining tasks: classi cation and regression, and descriptive data mining tasks: clustering, association rules and sequence analysis. The new-developed models, which are main contribution of the dissertation are comparable in performance with the best currently existing methods, and even better in some cases. Developed models are based on the support vector machine technique for classi cation and regression problems. À new approach of extracting the most important physicochemical properties that in uence the classi cation of MHC-binding ligands is also presented. For that purpose are developed new clustering-based classi cation models. The models are based on k-means clustering technique. The second part of the thesis concerns the establishment of rules and associations of T - cell epitopes that belong to di erent protein structures. The task of this part of research was to nd out whether disorder and hydropathy prediction methods could help in understanding epitope processing and presentation. The results of the application of an association rule technique and thorough analysis over large protein dataset where T cell epitopes, protein structure and hydropathy has been determined computationally, using publicly available tools, are presented. During the research on this theses new extendable open source software system that support bioinformatic research and have wide applications in prediction of various proteins characteristics is developed. A part of this thesis is described in the works [71][82][45][42][43][44][72][73] that are published or submitted for publications in several journals. The dissertation is organized as follows: In section1 is illustrated introduction to the problem of identifying T - cell epitopes, the importance of mathematical and computational methods in this area, vii as well as the importance of T - cell epitopes to the immune system and basis for functioning of the immune system. In section 2 are described in details data mining techniques that are used in the thesis for development of new models. Section 3 provides an overview of existing methods for predicting the T - cell epitopes and explains the work methodologies of existing models and methods. It pointed out the shortcomings of existing methods which have been the motivation for the development of new models for the T - cell epitope prediction. Some of the publicly available databases with the experimentally determined MHC binding peptides and T - cell epitope are described. In section 4 are presented new developed models for epitopes prediction. The developed models include three new encoding schemes for peptide sequences representation in the form of a vector which is more suitable as input to models based on the data mining techniques. Section 5 reports results of presented new classi cation and regression models. The new models are compared with each other as well as with currently existing methods for T cell epitope prediction. Section 6 presents the research results of the T - cell epitopes relationship with ordered and disordered regions in proteins. In the context of this chapter summary results are presented which are shown in more detail in the published works [71][82][45][44]. Section 7 concludes the dissertation with some discussion of the potential signi cance of obtained results and some directions for future work. URI: http://hdl.handle.net/123456789/4457 Files in this item: 1
doktorskaTezaDavorkaJandrlic.pdf ( 7.938Mb ) -
Karapandžić, Đorđe (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/142 Files in this item: 1
phdDjordjeKarapandzic.pdf ( 3.246Mb ) -
Doder, Dragan (Beograd , 2011)[more][less]
-
Andrejić, Vladica (Beograd , 2010)[more][less]
Abstract: U ovom radu posmatramo princip dualnosti (i jake dualnosti) za Osermanove mnogostrukosti i uopxtavamo ga za pseudo-Rimanov sluqaj. Osnovni ci je dokazati princip dualnosti za Osermanove mnogostrukosti u opxtem sluqaju ili konstrukcija eventualnih kon- traprimera. Za sada smo u sta u da damo samo rezultate pod speci- fiqnim dodatnim uslovima. Prva mogu nost je mali indeks pseudo- Rimanove mnogostrukosti, gde dokazujemo da jaka dualnost va i za Rimanove i Lorencove prostore. Druga mogu nost su prostori malih dimenzija gde dokazujemo da jaka dualnost va i kad dimenzija nije ve a od qetiri. Posled a olakxavaju a okolnost sa kojom radimo tiqe se malog broja sopstvenih vrednosti redukovanog Jakobijevog operatora, gde posmatramo dvolisno-Osermanove tenzore krivine. U tom sluqaju radimo sa jakim uslovima iz definicije kvazi-specijalnih Osermanovih tenzora krivine i elimo da doka emo da pod ima va i princip dualnosti. Konaqan rezultat je da skoro-specijalan Oser- manov tenzor krivine mora biti specijalan Osermanov. U nastavku postav amo obratan problem, te pokuxavamo da istra imo pod kojim uslovima algebarski tenzor krivine za koji va i princip dualnosti mora biti Osermanov. Potvrdan rezultat dobili smo u dimenziji tri, kao i u sluqaju kada se Fidlerova suma sastoji od samo jednog qlana. URI: http://hdl.handle.net/123456789/2479 Files in this item: 1
phdAndrejicVladica.pdf ( 513.6Kb ) -
Dajović, Slobodan (Belgrade)[more][less]
-
Đorđević, Radosav (Kragujevac , 1991)[more][less]
Abstract: The thesis consists of six chapters. Chapter 1 contains the structures, in which the probability logics are realized, and the basic methods of nonstandard analysis which are used in the other chapters. In Chapter 2 the syntax and semantics of the following probability logics are presented: the logic with the probability quantifiers L_Ap, the logic with the integral operators L_A_∫ , the logic with the operator of conditional expectation L_AE and adapted probability logic L_ad. Moreover, the certain important results about these logics are given. The problems of Barwise’s completeness, completeness, compactness, the existence of analytic and hyperfinite models for biprobability logics LA_P1_P2, LA_∫_1_∫_2 and L_ad in absolute continuous and singular cases are solved in Chapter 3. The many-probability logic BC{L_AP_i:i∊I}, I∊A obtained by Boolean combinations of probability logics L_AP is introduced and some model-theoretical properties of that logic are given in Chapter 4. In Chapter 5 the probability logic L^2AP∀ of second order is introduced, which is motivated by Keisler’ s problems with L_AP∀ and some topological logics. The problem of completeness for the logic L^2AP∀ is proved. In Chapter 6 cylinder probability algebras are introduced and some possibilities to solve problems for these algebras (which are characteristics of standard cylinder algebras, as the representation, axiomatization and decidability) are presented. URI: http://hdl.handle.net/123456789/189 Files in this item: 1
phdRadosavSDjordjevic.pdf ( 2.407Mb ) -
Djerasimović, Božidar (Belgrade)[more][less]
URI: http://hdl.handle.net/123456789/140 Files in this item: 1
phdBozidarPDjerasimovic.pdf ( 2.343Mb ) -
Stančić, Olivera (Beograd , 2018)[more][less]
Abstract: Hub Location Problems (HLP) represent an important class of optimiza- tion problems due to their numerous applications in many areas of real life. They often arise from practical situations that require routing of the flow from origin node (supplier) to the destination node (customer) under given conditions, such that the value of considered objective function is optimal. Hubs are special objects (nodes in the network) that represent centres for consolidation and flow collection between two selected locations - suppliers and customers. As transportation costs (per unit of flow) along the links that connect hub nodes are lower compared to other links in the network, directing the flow to hubs may lead to significant reductions of transportation cost in the network. The subject of this doctoral dissertation is one class of hub location problems, denoted as Hub Maximal Covering Problems (HMCPs) in the literature. The goal of HMCPs is to determine optimal locations for establishing certain number of hubs in order to maximize the total flow between all the covered origin-destination pairs, under the assumption of binary or partial covering. Three variants of the hub maximal covering problem are considered: uncapacitated single allocation p -hub maximal covering problem (USApHMCP), uncapacitated multiple allocation p -hub maximal covering problem (UMApHMCP) and uncapacitated r -allocation p -hub maximal covering problem (UrApHMCP). Note that the UrApHMCP has not been studied in the literature so far. All three considered problems are proven to be NP- hard. In case of USApHMCP, for the given set of hubs, the obtained sub-problem of optimal allocation of non-hub nodes by established hubs is also NP-hard. In this dissertation, new mathematical models for USApHMCP with binary and partial covering are proposed. The main advantage of the newly proposed models, in respect to existing ones from the literature, is the fact that small modifications of the new models enable their transformation to new models for p -hub maximal covering problems with different allocation schemes. More precisely, new models for UMApHMCP and UrApHMCP can be obtained from the newly proposed mod- els for USApHMCP in both coverage cases. All proposed models for USApHMCP and UMApHMCP are compared with the existing ones from the literature in the terms of efficiency within the framework of exact CPLEX 12.6 solver. Several hub data sets from the literature are used in numerical experiments when comparing the formulations. The obtained experimental results indicate that new models for UMApHMCP with both binary and partial coverage show the best performance in terms of solutions’ quality and execution times. For UrApHMCP and both coverage criteria, three mathematical models are proposed, and compared in terms of effi- ciency using the exact CPLEX 12.6 solver. It turns out that the exact solver finds optimal or feasible solutions only for small-size problem instances. Having in mind the complexity of all three problems under consideration and the results obtained by CPLEX 12.6 solver, the conclusion is that, in practice, exact methods can not provide solutions for large problem dimensions. For this reason, it was necessary to implement adequate heuristic or metaheuristic methods, in order to obtain high-quality solutions in short execution times, even in the case of large problem dimensions. Up to now, only simple but insufficiently effective heuris- tic methods for solving USApHMCP and UMApHMCP with binary coverage have been proposed in the literature, while the HMCP variants with partial coverage have not been previosly solved by using metaheuristic methods. As UrApHMCP with binary and partial coverage has not been previously considered in the litera- ture, no solution methods suggested for this problem existed up to now. Inspired by previous successful applications of variable neighborhood search method (VNS) to other hub location problems from the literature, this metaheuristic approach is applied to the considered HMCP problems. In this dissertation, several variants of VNS metaheuristic are designed and implemented: General Variable Neighborhood Search (GVNS) for USApHMCP, Basic Variable Neighborhood Search (BVNS) for UMApHMCP and a variant of General Variable Neighborhood Search (GVNS-R) for UrApHMCP. In the case of UrApHMCP, two additional metaheuristic meth- ods are proposed: Greedy Randomized Adaptive Search Procedure with Variable Neighborhood Descent (GRASP-VND) and Genetic Algorithm (GA). Constructive components of all proposed metaheuristics are adapted to the characteristics of the considered problems. Experimental study was conducted on the existing hub data sets from the lit- erature, which include instances with up to 1000 nodes in the network. The ob- tained results show that the proposed metaheuristics for the considered problems reach all known optimal solutions previously obtained by CPLEX 12.6 solver or establish new best-known solutions in significantly shorter CPU time compared to CPLEX 12.6. The proposed GVNS and BVNS metaheuristics quickly reach all known optimal solutions on small-size problem instances when solving USApHMCP and UMApHMCP, respectively. In the case of large-size problem instances, which have not been previously used for testing purposes for these problems, the proposed GVNS and BVNS return their best solutions in short execution times. The results obtained by the proposed GVNS-R and GRASP-VND for UrApHMCP on large-size problem instances indicate their effectiveness in both coverage cases. The proposed GA method showed to be successful only for UrApHMCP in binary covering, on instances up to 200 nodes. The variants of hub maximal covering problems considered in this dissertation are important from both theoretical and practical points of view. The new mathe- matical models proposed in this dissertation for the considered variants of HMCP, represent a scientific contribution to the theory of hub location problems, mathemat- ical modeling and optimization. Designed and implemented metaheuristic methods for solving the studied variants of HMCP are the scientific contribution to the field of optimization methods for solving location problems, as well as the development of software. The considered variants of HMCP have numerous applications in the optimization of telecommunication and transport systems, air passenger and goods transport, emergency services, postal and other delivery systems, so that the results obtained in this doctoral dissertation can be applied in practice, partially or com- pletely. URI: http://hdl.handle.net/123456789/4750 Files in this item: 1
StancicOliveradisertacija.pdf ( 1.688Mb ) -
Stojanović, Stevan (Belgrade , 1969)[more][less]
-
Berisha, Muharrem (Pristina , 1979)[more][less]
-
Mateljević, Miodrag (Belgrade)[more][less]
-
Melentijević, Petar (Beograd , 2018)[more][less]
Abstract: In this thesis we study sharp estimates of gradients and operator norm estimates in harmonic function theory. First, we obtain Schwarz-type inequalities for holomorphic mappings from the unit ball B n to the unit ball B m , and then analoguous inequalities for holomorphic functions on the disk D without zeros and pluriharmonic functions from the unit ball B n to ( − 1 , 1) . These extend results from [ 32 ] and [ 18 ]. Also, we give a new proof of the fact that positive harmonic function in the upper-half plane is a contraction with resprect to hyperbolic metrics on both H and R + ([ 47 ]). Besides that, in the second chapter, we construct the examples to show that the analoguous does not hold for the higher-dimensional upper-half spaces. All mentioned results are from the authors’ paper [55]. In the third chapter we intend to calculate the exact seminorm of the weighted Berezin transform considered as an operator from L ∞ ( B n ) to the ”smooth” Bloch space ([57]). The fourth chapter contains results concerning Bergman projection. We solve the problem posed by Kalaj and Marković in [ 28 ] on determining the exact seminorm of the Bergman projections from L ∞ ( B n ) to the B ( B n ) . The crucial obstacle is the fact that B ( B n ) is equipped with M− invariant gradient seminorm. Also, we provide the sharp gradient estimates of the Bergman projection of an L p function in the unit ball B n , as well as its consequences on Cauchy projection and certain gradient estimates for the functions from the Hardy and Bergman spaces.We obtain the exact values of the Bloch’s seminorms and norms for the Cauchy projection on L ∞ ( S n ) . These results are based on the papers [56] and [58]. The last chapter contains the proof of the one part of Hollenbeck-Verbitsky conjecture from [ 26 ]. Exactly, we find the exact norms of ( | P + | s + | P − | s ) 1 s for 0 < s ≤ 2 on L p ( T ) , where P + is the Riesz projection and P − = I − P + . Also we give the appropriate dual estimates and prove that they are sharp. The paper [ 45 ] is motivated by the results from [25] and [33]. URI: http://hdl.handle.net/123456789/4749 Files in this item: 1
doktorat_Petar_merged.pdf ( 1.507Mb ) -
Popović, Biljana (Belgrade)[more][less]